1/2h=1/h-5

Solution for 1/2h=1/h-5 equation:

1/2h=1/h-5

We move all terms to the left:

1/2h-(1/h-5)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: h-5)!=0

h∈R


We get rid of parentheses

1/2h-1/h+5=0

We calculate fractions


h/2h^2+(-2h)/2h^2+5=0

We multiply all the terms by the denominator


h+(-2h)+5*2h^2=0

Wy multiply elements

10h^2+h+(-2h)=0

We get rid of parentheses

10h^2+h-2h=0

We add all the numbers together, and all the variables

10h^2-1h=0

a = 10; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·10·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*10}=\frac{0}{20}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*10}=\frac{2}{20}
=1/10
$